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General Physics (PHY 2130)
Lecture 8
•  Forces
•  Newton’s Laws of Motion
http://www.physics.wayne.edu/~apetrov/PHY2130/
Classical Mechanics
Describes the relationship between the
motion of objects in our everyday world and
the forces acting on them
►  Conditions when Classical Mechanics does
not apply
► 
  very tiny objects (< atomic sizes)
  objects moving near the speed of light
Forces
►  Usually
think of a force
as a push or pull
►  Vector
►  May
quantity
be contact
or
long range (field) force
Fundamental Forces
►  Types
 
 
 
 
Strong nuclear force
Electromagnetic force
Weak nuclear force
Gravity
►  Characteristics
  All field forces
  Listed in order of decreasing strength
  Only gravity and electromagnetic in mechanics
Measuring the force
How can a force be measured?
One way is with a spring scale.
5
Units of Force
► SI
unit of force is a Newton (N)
kg m
1N ≡ 1 2
s
Units of force
► 1
SI
Newton (N=kg m/ s2)
CGS
Dyne (dyne=g cm/s2)
US Customary
Pound (lb=slug ft/s2)
N = 105 dyne = 0.225 lb
More about forces
► What
if there is more than one force acting
on a body?
  Different forces can be added vectorially
► The
net force is the vector sum of all the
forces acting on a body:

   
Fnet = ∑ F = F1 + F2 + F3 +…
all
7
In the drawing, what is the vector sum of forces A + B+ C if each grid
square is 2 N on a side?
(Answer 2N to East)
8
Free Body Diagram
► Must
identify all the forces acting on the
object of interest
► Choose an appropriate coordinate system
► If the free body diagram is incorrect, the
solution will likely be incorrect
Free Body Diagram
  Draw an idealization of the body in question (a dot, a box,…). You will need
one free body diagram for each body in the problem that will provide useful
information for you to solve the given problem.
  Choose an appropriate coordinate system!!!
  Indicate only the forces acting on the body. Label the forces appropriately. Do
not include the forces that this body exerts on any other body.
  You may indicate the direction of the body’s acceleration or direction of
motion if you wish, but it must be done well off to the side of the free body
diagram.
10
Example: Free Body Diagram
Real life
Free body diagram
y

T
0

Fg
x
11
Newton’s First Law
► If
no forces act on an object, it continues in
its original state of motion; that is, unless
something exerts an external force on it, an
object at rest remains at rest and an object
moving with some velocity continues with
that same velocity.
Newton’s First Law, cont.
► External
force
  any force that results from the interaction
between the object and its environment
► Alternative
Law
statement of Newton’s 1st
  When there are no external forces acting on
an object, the acceleration of the object is
zero.
Inertia and Mass
►  Inertia
is the tendency of an object to continue in
its original motion
►  Mass is a measure of the inertia, i.e resistance of
an object to changes in its motion due to a force
►  Recall: mass is a scalar quantity
Units of mass
SI
kilograms (kg)
CGS
grams (g)
US Customary slug (slug)
Inertia and Mass: Two Examples
Runaway train
►  Inertia
is the tendency
of an object to continue
in its original motion
►  Mass is a measure of
the inertia, i.e
resistance of an object
to changes in its
motion due to a force
Inertia and Mass: Two Examples
Seatbelt
►  Inertia
is the tendency of
an object to continue in
its original motion
►  Mass is a measure of the
inertia, i.e resistance of
an object to changes in
its motion due to a force
Newton’s Second Law
►  The
acceleration of an object is directly
proportional to the net force acting on it and
inversely proportional to its mass.
F
∑
a∝
m
or
∑ F = ma
  F and a are both vectors
►  Can
also be applied three-dimensionally
  acceleration can also be caused by change of the
direction of velocity
Newton’s Second Law
► Note:
∑ F represents the vector sum of
all external forces acting on the object.
►  Since N2ndL is a vector equation, we can
always write it in terms of components:
$ Fx = ma x
!
∑ F = ma : #Fy = ma y
! F = ma
z
" z
Example: force on the bullet
A 5.0-g bullet leaves the muzzle of a rifle with a speed of 320 m/s.
What total force (assumed constant) is exerted on the bullet while
it is traveling down the 1-m-long barrel of the rifle?
Given:
m=5g
= 0.005 kg
vf = 320 m/s
vi = 0 m/s
Δx = 1 m
Find:
F=?
Solution:
F
Idea: let’s use 2nd Newton’s law F=ma. To do so, we would
need to calculate bullet’s acceleration.
v 2f = vi2 + 2a Δx
or
v 2f
(320 m s)2
a=
=
= 51200 m s 2
2 Δx
2(1m)
Now, force:
F = m a = 0.005kg × 51200 m s 2 = 256N
ConcepTest
A car rounds a curve while maintaining a constant
speed. Is there a net force on the car as it rounds the
curve?
1. No—its speed is constant.
2. Yes.
3. It depends on the sharpness of the curve
and the speed of the car.
4. It depends on the driving experience of the
driver.
ConcepTest
A car rounds a curve while maintaining a constant
speed. Is there a net force on the car as it rounds the
curve?
1. No—its speed is constant.
2. Yes.  
3. It depends on the sharpness of the curve
and the speed of the car.
4. It depends on the driving experience of the
driver.
Note: Acceleration is a change in the speed and/or direction
of an object. Thus, because its direction has changed,
the car has accelerated and a force must have been
exerted on it.
Newton’s Third Law
► If
two objects interact, the force F12 exerted
by object 1 on object 2 is equal in
magnitude but opposite in direction to the
force F21 exerted by object 2 on object 1.
  Equivalent to saying a single isolated force
cannot exist
Example: Newton’s Third Law
►  Consider
collision of two
spheres
►  F12 may be called the
action force and F21 the
reaction force
  Actually, either force can
be the action or the
reaction force
►  The
action and reaction
forces act on different
objects
Example 1: Action-Reaction Pairs
►  n
and n’
  n is the normal force,
the force the table
exerts on the TV
  n is always
perpendicular to the
surface
  n’ is the reaction – the
TV on the table
  n = - n’
Example 2: Action-Reaction pairs
►  Fg
and Fg’
  Fg is the force the
Earth exerts on the
object
  Fg’ is the force the
object exerts on the
earth
  Fg = -Fg’
Forces Acting on an Object
►  Newton’s
Law uses
the forces acting on an
object
►  n and Fg are acting on
the object
►  n’ and Fg’ are acting
on other objects
ConcepTest
Consider a person standing in an elevator that is accelerating
upward. The upward normal force N exerted by the elevator
floor on the person is
1.
2.
3.
4.
larger than
identical to
smaller than
equal to zero, i.e. irrelevant to
the downward weight W of the person.
ConcepTest
Consider a person standing in an elevator that is accelerating
upward. The upward normal force N exerted by the elevator
floor on the person is
1.
2.
3.
4.
larger than  
identical to
smaller than
equal to zero, i.e. irrelevant to
the downward weight W of the person.
Note: In order for the person to be accelerated upward, the
normal force exerted by the elevator floor on her must
exceed her weight.
Three Newton’s laws
1.  If no forces act on an object, it continues in its original
state of motion; that is, unless something exerts an
external force on it, an object at rest remains at rest and
an object moving with some velocity continues with that
same velocity.
2.  The acceleration of an object is directly proportional to the
net force acting on it and inversely proportional to its
mass.
3.  If two objects interact, the force F12 exerted by object 1
on object 2 is equal in magnitude but opposite in direction
to the force F21 exerted by object 2 on object 1.